Also, Ben Sheets threw live batting practice for the first time and impressed the coaching staff with his velocity.
"He threw the first pitch right by somebody," A's manager Bob Geren said.
Tomko, who finished the season with Oakland last year, will continue to rehab an irritated nerve in his right arm that ended his 2009 season prematurely. He'll report to the minor league camp and is expected to be ready to pitch by May.
Jennings, the 2002 NL Rookie of the Year, pitched for the Texas Rangers last year and was eager to get started this spring.
"I packed a couple of suitcases last night and caught a 7 a.m. flight [from Dallas] this morning," Jennings said minutes after arriving at Phoenix Muni on Sunday. "It's been crazy. I've been working out at home trying to keep up with everybody else in spring training waiting for an opportunity."
Jennings, sporting the number 77, braved a light drizzle to play catch with A's pitching coach Curt Young in the outfield. He hopes to throw a bullpen session Monday.
"I want to jump into some kind of routine," he said. "This is the healthiest I've felt since 2005."
Jennings endured elbow problems the past three years as he pitched for the Houston Astros and Texas Rangers. He was converted into a relief pitcher with the Rangers last year and was 2-4 with a 4.13 ERA in 44 appearances.
"He's experienced, he's a former Rookie of the Year and he had some great years for Colorado," Geren said. "He pitched well for the Rangers last year and he's healthy. We're happy to have him."
Jennings was 9-13 with a 3.78 ERA despite the NL's third-lowest offensive support of 4.03 runs per game in his final season with the Rockies in 2006.
He was 20-9 in his first 39 starts with Colorado, which included a sparkling debut on Aug. 23, 2001, when he threw an 8-hitter at the New York Mets in a 10-0 victory. He led off the ninth with a home run and had three hits in the game.
"I felt I threw the ball well last year," Jennings said. "I started until last year and was put in a relief role. It was brand new for me and I proved to myself I could do it."
The A's plan to stretch him out as a possible starter or long relief.
"He's been a starter so we know he's a multiple-inning guy," Geren said. "We want to get him slotted in somewhere and get him going."
Jennings played with Jack Cust on the Rockies and has known Sheets since they were both in college.
"We have a history," Jennings said.
It turns out Jennings, playing for Baylor, hit a walk-off home run against Sheets, pitching for Louisiana-Monroe.
"I think I let him do it," Sheets joked. "I had a date that night."
Geren also said that right-hander Trevor Cahill, slated to start the first game of spring training Thursday at the Cubs, threw the best he's seen.
"As far as throwing all of his pitches combined, it was a solid outing," Geren said.